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research article
Trace coordinates of Teichmüller space of Riemann surfaces of signature $(0,4)$
Summary: We explicitly give $calT$, the Teichmüller space of four-holed spheres (which we call $X$ pieces) in trace coordinates, as well as its modular group and a fundamental domain for the action of this group on $calT$ which is its moduli space. As a consequence, we see that on any hyperbolic Riemann surface, two closed geodesics of lengths smaller than $2operatornamearccosh(2)$ intersect at most once; two closed geodesics of lengths smaller than $2operatornamearccosh(3)$ are both non-dividing or intersect at most once.
Type
research article
Authors
Publication date
2005
Published in
Volume
9
Start page
46
End page
75
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
December 3, 2010
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